A support block is acted upon by two forces as shown in fig. Knowing that the coefficient of friction between the block & the incline are $\mu_s = 0.35$, $\mu_k = 0.25$. Determine the force P required to prevent it from slipping down.[Figure: a b…

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Q.1 (c) A support block is acted upon by two forces as shown in fig. Knowing that the coefficient of friction between the block & the incline are μ_s = 0.35 , μ_k = 0.25 . Determine the force P required to prevent it from slipping down. [Figure: a block rests on an incline that slopes downward to the right at 25° to the horizontal. A vertical load of 800 N acts downward on the block, and a horizontal force P acts on the block pointing to the left (i.e. pushing the block towards the uphill side / into the incline).]

Doubtly AI · Accepted Answer

Given: W = 800 N (vertical), P horizontal (towards the uphill side), θ = 25^° , μ_s = 0.35 (impending motion, so static coefficient is used). The block tends to slip down the plane, so friction F acts up the plane and F = μ_s N . Resolve perpendicular to plane: N = 800cos25^° + Psin25^° = 725.05 + 0.4226P Resolve along plane: Pcos25^° + μ_s N = 800sin25^° 0.9063P + 0.35(725.05 + 0.4226P) = 338.09 0.9063P + 0.1479P + 253.77 = 338.09 ⇒ 1.0542P = 84.33 Answer: P ≈ 80 N (minimum horizontal force to prevent slipping down; μ_k is not needed because motion is only impending).

A support block is acted upon by two forces as shown in fig. Knowing that the coefficient of friction between the block & the incline are \(\mu_s = 0.35\), \(\mu_k = 0.25\). Determine the force P required to prevent it from slipping down.[Figure: a b…

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